Hidden Markov Models in Python¶

Model sequences and uncover patterns in time series data¶


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Introduction¶

Hidden Markov Models (HMMs) are powerful statistical tools used in temporal pattern recognition, such as speech, bioinformatics, and finance. They model systems where the states are hidden but produce observable outputs. Despite their complexity, Python libraries make implementing HMMs cleanly and effectively possible.

Why it’s so important¶

Helps model sequences where underlying patterns are not directly observable.
Widely used in fields like natural language processing, genomics, and market prediction.
Builds a foundation for mastering other sequence models like RNNs and Transformers.

Code Implementation¶

In [2]:

!pip install hmmlearn

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Installing collected packages: hmmlearn
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In [4]:

from hmmlearn.hmm import CategoricalHMM
import numpy as np

# Example: Weather states (0 = Sunny, 1 = Rainy)
observations = np.array([[0], [1], [0], [1], [1], [0]])

model = CategoricalHMM(n_components=2, n_iter=100)
model.fit(observations)

logprob, hidden_states = model.decode(observations, algorithm="viterbi")

print("Most likely hidden states:", hidden_states)

Most likely hidden states: [1 1 1 1 1 1]

Understanding the Code, Hidden Markov Models with CategoricalHMM¶

This code demonstrates how to use a Hidden Markov Model (HMM) with categorical (discrete) observations to uncover hidden states from a sequence of events. In this example, you're modeling weather states like Sunny (0) and Rainy (1) using hmmlearn's CategoricalHMM.

What Each Part Does¶

Input Observations

In [5]:

observations = np.array([[0], [1], [0], [1], [1], [0]])

This is a sequence of observed weather conditions: Sunny, Rainy, Sunny, etc.

The values must be in a 2D array format ([[0], [1], ...]), as required by hmmlearn.

Model Initialization

In [6]:

model = CategoricalHMM(n_components=2, n_iter=100)

n_components=2 sets the number of hidden states (for example, “Dry” and “Wet” weather systems).
n_iter=100 allows up to 100 iterations during training to ensure the model converges.

Training the Model

In [7]:

model.fit(observations)

Out[7]:

CategoricalHMM(n_components=2, n_features=np.int64(2), n_iter=100,
               random_state=RandomState(MT19937) at 0x7BF73FEA1540)

In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.

This learns the model's parameters (start probabilities, transition probabilities, and emission probabilities) from the observation sequence.

Decoding Hidden States

In [9]:

logprob, hidden_states = model.decode(observations, algorithm="viterbi")

Uses the Viterbi algorithm to find the most probable sequence of hidden states that explains the observations.
logprob is the log-likelihood of the sequence.
hidden_states is a 1D array like [1, 0, 1, 0, 0, 1] representing the inferred hidden states.

Output

In [10]:

print("Most likely hidden states:", hidden_states)

Most likely hidden states: [0 1 0 1 1 0]

Displays the most probable hidden states behind the weather sequence.

What's the Use Case?¶

Hidden Markov Models are widely used for:
Speech recognition
Biological sequence analysis (DNA, proteins)
Financial modeling
Natural Language Processing (e.g., part-of-speech tagging)

Conclusion¶

Hidden Markov Models may seem mathematically dense, but Python makes them approachable. Once understood, they open doors to complex applications where sequence and state prediction are crucial. Thanks for reading my article, let me know if you have any suggestions or similar implementations via the comment section. Until then, see you next time. Happy coding!

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